2.3.56 Problems 5501 to 5600

Table 2.643: Main lookup table. Sorted by time used to solve.

#	ID	ODE	Solved?	Maple	Mma	Sympy	time(sec)
5501	10237	\begin{align*} y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5502	10774	\begin{align*} \left (2+x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5503	10797	\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +30 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5504	10937	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x +28 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5505	11082	\begin{align*} 2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5506	11094	\begin{align*} \left (-z^{2}+1\right ) y^{\prime \prime }-3 z y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5507	11695	\begin{align*} a {y^{\prime }}^{2}-y^{\prime } y-x&=0 \\ \end{align*}	✓	✓	✓	✗	0.289
5508	15689	\begin{align*} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y&={\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.289
5509	16025	\begin{align*} x^{\prime }&=-3 x \\ y^{\prime }&=x-3 y \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.289
5510	16987	\begin{align*} y^{\prime }&=\frac {-x^{2}+x}{\left (x +1\right ) \left (x^{2}+1\right )} \\ \end{align*}	✓	✓	✓	✓	0.289
5511	17738	\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✓	0.289
5512	18371	\begin{align*} y^{\prime }&=-y x +1 \\ y \left (0\right ) &= 0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.289
5513	19752	\begin{align*} y^{\prime \prime }+12 y&=7 y^{\prime } \\ \end{align*}	✓	✓	✓	✓	0.289
5514	22316	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.289
5515	22618	\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.289
5516	22742	\begin{align*} y^{\prime \prime }-y&=2 x^{4}-3 x +1 \\ \end{align*}	✓	✓	✓	✓	0.289
5517	23044	\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&={\mathrm e}^{4 x} \\ \end{align*}	✓	✓	✓	✓	0.289
5518	23117	\begin{align*} y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+y\right ) \\ \end{align*}	✓	✓	✓	✗	0.289
5519	24656	\begin{align*} y^{\prime \prime }+36 y&=\cos \left (6 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.289
5520	24668	\begin{align*} y^{\prime \prime }+16 y&=48 \cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.289
5521	24672	\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&=\sin \left (2 x \right ) {\mathrm e}^{-x} \\ \end{align*}	✓	✓	✓	✓	0.289
5522	1068	\begin{align*} y^{\prime \prime }+y^{\prime } x +y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.290
5523	1267	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=0 \\ y \left (0\right ) &= \alpha \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.290
5524	1738	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ y \left (0\right ) &= k_{0} \\ y^{\prime }\left (0\right ) &= k_{1} \\ \end{align*}	✓	✓	✓	✓	0.290
5525	2213	\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right ) \\ \end{align*}	✓	✓	✓	✓	0.290
5526	5409	\begin{align*} {y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
5527	6094	\begin{align*} 6 y+2 y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
5528	6189	\begin{align*} -2 y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
5529	7278	\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\ \end{align*}	✓	✓	✓	✓	0.290
5530	7594	\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= -12 \\ \end{align*}	✓	✓	✓	✓	0.290
5531	7813	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.290
5532	7841	\begin{align*} y^{\prime \prime }+2 x^{2} y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.290
5533	10676	\begin{align*} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
5534	10863	\begin{align*} 5 y^{\prime \prime }-2 y^{\prime } x +10 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
5535	10966	\begin{align*} 18 x^{2} \left (x +1\right ) y^{\prime \prime }+3 x \left (x^{2}+11 x +5\right ) y^{\prime }-\left (-5 x^{2}-2 x +1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
5536	12551	\begin{align*} 9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y&=0 \\ \end{align*}	✓	✓	✓	✗	0.290
5537	14397	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=x+3 y \\ \end{align*}	✓	✓	✓	✓	0.290
5538	15245	\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&={\mathrm e}^{-\frac {t}{2}} \delta \left (-1+t \right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.290
5539	16140	\begin{align*} y^{\prime \prime }+3 y&=5 \delta \left (t -2\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.290
5540	16188	\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ y \left (0\right ) &= 3 \\ \end{align*}	✓	✓	✓	✓	0.290
5541	16838	\begin{align*} 6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.290
5542	17361	\begin{align*} y^{\prime \prime }+6 y^{\prime }+18 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.290
5543	18005	\begin{align*} x {y^{\prime }}^{2}&={\mathrm e}^{\frac {1}{y^{\prime }}} \\ \end{align*}	✓	✓	✓	✗	0.290
5544	19030	\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}	✓	✓	✓	✓	0.290
5545	24665	\begin{align*} y^{\prime \prime }+16 y&=14 \cos \left (3 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.290
5546	452	\begin{align*} y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.291
5547	1077	\begin{align*} y^{\prime \prime }-x^{2} y^{\prime }-3 y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.291
5548	7832	\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ y^{\prime \prime }\left (0\right ) &= 3 \\ \end{align*} Using Laplace transform method.	✓	✓	✓	✓	0.291
5549	8806	\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&=g \left (t \right ) \\ \end{align*}	✓	✓	✓	✓	0.291
5550	10958	\begin{align*} y^{\prime \prime }-3 y^{\prime } x +\left (2 x^{2}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.291
5551	15140	\begin{align*} y^{\prime \prime }&=y+x^{2} \\ \end{align*}	✓	✓	✓	✓	0.291
5552	15164	\begin{align*} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}+2\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.291
5553	18345	\begin{align*} x^{\prime \prime }+2 x^{\prime }+x&=0 \\ \end{align*}	✓	✓	✓	✓	0.291
5554	18652	\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=x-2 y \\ \end{align*}	✓	✓	✓	✓	0.291
5555	18685	\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*}	✓	✓	✓	✓	0.291
5556	19155	\begin{align*} x \left (x^{2} y^{\prime }+2 y x \right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 x y^{\prime } y+4 y^{2}-1&=0 \\ \end{align*}	✗	✗	✗	✗	0.291
5557	20882	\begin{align*} y^{\prime }&=2 y x -x^{3} \\ y \left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.291
5558	22480	\begin{align*} 2 y^{\prime \prime \prime \prime }&={\mathrm e}^{x}-{\mathrm e}^{-x} \\ y \left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}	✓	✓	✓	✓	0.291
5559	23320	\begin{align*} 4 y^{\prime \prime }-3 y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.291
5560	24594	\begin{align*} y^{\prime \prime }-y&=\cos \left (4 x \right ) \\ \end{align*}	✓	✓	✓	✓	0.291
5561	24659	\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=15 \,{\mathrm e}^{x} \\ \end{align*}	✓	✓	✓	✓	0.291
5562	25324	\begin{align*} y^{\prime \prime }-y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.291
5563	25332	\begin{align*} \left (t^{2}+1\right ) y^{\prime \prime }-4 t y^{\prime }+6 y&=0 \\ \end{align*} Series expansion around \(t=0\).	✓	✓	✓	✓	0.291
5564	522	\begin{align*} 16 x^{2} y^{\prime \prime }-\left (-144 x^{3}+5\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
5565	1063	\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= -2 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.292
5566	1270	\begin{align*} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
5567	1273	\begin{align*} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
5568	3510	\begin{align*} \left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y&=0 \\ \end{align*} Series expansion around \(z=0\).	✓	✓	✓	✓	0.292
5569	6029	\begin{align*} \left (b x +a \right ) y+2 a x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}	✓	✓	✓	✗	0.292
5570	6323	\begin{align*} y^{\prime \prime }&=g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime } \\ \end{align*}	✗	✗	✗	✗	0.292
5571	8907	\begin{align*} y^{\prime \prime }+2 i y^{\prime }+y&=x \\ \end{align*}	✓	✓	✓	✓	0.292
5572	9381	\begin{align*} y^{\prime \prime }+y x&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.292
5573	9497	\begin{align*} y^{\prime \prime }-y^{\prime }&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.292
5574	10689	\begin{align*} 6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.292
5575	10929	\begin{align*} x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+4\right ) y^{\prime }+2 \left (-x^{2}+1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.292
5576	11165	\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
5577	13728	\begin{align*} y^{\prime \prime } x +a y^{\prime }+b \,x^{n} y&=0 \\ \end{align*}	✓	✓	✓	✗	0.292
5578	14377	\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=2 y \\ \end{align*}	✓	✓	✓	✓	0.292
5579	15110	\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\ \end{align*}	✓	✓	✓	✗	0.292
5580	15460	\begin{align*} x^{\prime }&=12 x+18 y \\ y^{\prime }&=-8 x-12 y \\ \end{align*}	✓	✓	✓	✓	0.292
5581	20932	\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=y \\ \end{align*}	✓	✓	✓	✓	0.292
5582	22193	\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.292
5583	22289	\begin{align*} y^{\prime \prime }+y&=x \\ y \left (\frac {\pi }{2}\right ) &= \frac {\pi }{2} \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}	✓	✓	✓	✓	0.292
5584	22917	\begin{align*} x^{\prime }+4 x+3 y^{\prime }+4 y&=0 \\ x^{\prime }+2 x+2 y^{\prime }+2 y&=0 \\ \end{align*} With initial conditions \begin{align*} x \left (0\right ) &= -1 \\ y \left (0\right ) &= 6 \\ \end{align*}	✓	✓	✓	✓	0.292
5585	23306	\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
5586	24548	\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&=50 x +13 \,{\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.292
5587	25560	\begin{align*} m y^{\prime \prime }+b y^{\prime }+k y&=0 \\ \end{align*}	✓	✓	✓	✓	0.292
5588	1075	\begin{align*} 3 y^{\prime \prime }+y^{\prime } x -4 y&=0 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.293
5589	1081	\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*} Series expansion around \(x=0\).	✓	✓	✓	✓	0.293
5590	2234	\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=F \left (x \right ) \\ \end{align*}	✓	✓	✓	✓	0.293
5591	2376	\begin{align*} y^{\prime \prime }+y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
5592	3324	\begin{align*} y&=y^{\prime } x +{y^{\prime }}^{2} \\ \end{align*}	✓	✓	✓	✓	0.293
5593	3585	\begin{align*} y^{\prime }&=\ln \left (x \right ) x^{2} \\ y \left (1\right ) &= 2 \\ \end{align*}	✓	✓	✓	✓	0.293
5594	7783	\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\ \end{align*}	✓	✓	✓	✓	0.293
5595	8913	\begin{align*} 6 y^{\prime \prime }+5 y^{\prime }-6 y&=x \\ \end{align*}	✓	✓	✓	✓	0.293
5596	9048	\begin{align*} y^{\prime }&=2 x \\ \end{align*}	✓	✓	✓	✓	0.293
5597	10695	\begin{align*} x^{2} y^{\prime \prime }+x \left (-x +3\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
5598	10724	\begin{align*} x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y&=0 \\ \end{align*}	✓	✓	✓	✗	0.293
5599	11670	\begin{align*} {y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}	✓	✓	✓	✓	0.293
5600	12605	\begin{align*} y^{\prime \prime }&=-\frac {a y}{x^{4}} \\ \end{align*}	✓	✓	✓	✓	0.293